The present invention relates to a frequency and timing synchronization circuit to be applied to a TDMA (Time Division Multiple Access) receiver making use of a chirp signal.
In a radio communication system such as a mobile communication system, where high-speed digital signals are transmitted through multi-paths changing their status every moment, it is very important for a receiver how to quickly and exactly establish initial synchronization of detection frequency and symbol timings with a receiving radio signal even in a low C/N (Carrier to Noise) ratio.
In a Japanese patent application entitled xe2x80x9cFrequency Correction Apparatusxe2x80x9d and laid open as a Provisional Publication No. H09-008765 (hereinafter called the first prior art), there is disclosed a method of correcting a reference frequency for detecting an OFDM (Orthogonal Frequency Division Multiplex) signal.
The frequency correction apparatus of the first prior art comprises a frequency converter having a controllable local oscillator for converting the OFDM radio-frequency signal into an intermediate-frequency signal, a quadrature demodulator for splitting the intermediate-frequency signal into an in-phase and a quadrature-phase signal, a complex FFT (Fast Fourier Transform) circuit for performing complex Fourier transformation of the in-phase and the quadrature-phase signal, and a power measurement circuit for obtaining a frequency distribution of power spectrums of the OFDM signal in a frequency domain from the output of the complex FFT circuit.
By detecting a center position of the frequency distribution when multi-carriers are arranged symmetrically to a center frequency of the OFDM signal in the frequency domain, or by detecting a position of a reference carrier when it is inserted in the OFDM signal with an intensity different to other carriers, the actual center frequency of the OFDM signal is determined and the local oscillator is feedback-controlled for acquiring frequency synchronization with the receiving signal, in the first prior art.
In another Japanese patent application entitled xe2x80x9cA Frequency Error Detection Circuit by Detecting a Correlation Peakxe2x80x9d and laid open as a Provisional Publication No. H09-200081 (hereinafter called the second prior art), a method of detecting a frequency error for controlling an AFC (Automatic Frequency Control) circuit is disclosed to be applied to a DSSS (Direct Sequence Spread Spectrum) receiver.
The frequency error detection circuit according to the second prior art comprises;
a first complex code generator for generating a first complex code which is obtained by giving a certain frequency offset to a pseudo random scramble code toward a positive side,
a second complex code generator for generating a second complex code obtained by giving the same frequency offset to the pseudo random scramble code toward a negative side,
a first and a second complex matched filter each calculating complex correlation of a base-band complex signal obtained through a quadrature demodulator with the first complex code and. the second complex code;
a peak timing detector for outputting a peak timing for every symbol where either or both of outputs of the first and the second complex matched filter show a maximum power value,
a first and a second peak average detector for outputting a first and a second peak average by calculating averages, for several symbols, of peak values which are extracted from outputs of the first and the second complex matched filter at each peak timing detected by the peak timing detector,
a first and a second power calculator for calculating power values of the first and the second peak average, respectively,
a power difference calculator for obtaining a normalized power difference by dividing a difference between outputs of the first and the second power calculator by a sum thereof, and
a frequency error converter for outputting a frequency error corresponding to the normalized power difference referring to a table memory.
The complex matched filter functions as a band-pass filter. Therefore, the power value of the first peak average becomes larger than that of the second peak average when a positive frequency error remains in the base-band complex signal, and vice versa, which is detected by the frequency error converter and converted into the frequency error to be fed back to the quadrature detector, in the frequency error detection circuit of the second prior art.
There is also a method of establishing frequency and timing synchronization making use of a chirp signal, which is to be applied to a mobile terminal, for example, receiving a SCH (Synchronization Channel) signal according to the TDMA communication system.
FIG. 3 is a block diagram illustrating a conventional frequency and timing synchronization circuit 104 making use of the chirp signal.
The frequency and timing synchronization circuit 104 of FIG. 3 comprises a chirp signal generator 6, a demodulator 7 and a detector unit 9.
From a transmitter 1, a radio signal, wherein certain symbols are scrambled with a chirp signal s(t) represented by following equation (1), is transmitted.                                                                         s                ⁡                                  (                  t                  )                                            =                                                2                                ⁢                                  cos                  ⁡                                      (                                                                  π                        ⁢                                                  xe2x80x83                                                ⁢                                                  t                          2                                                                                            μ                        ⁢                                                  xe2x80x83                                                ⁢                                                  T                          2                                                                                      )                                                                                                                          =                                                1                                      2                                                  ⁢                                  {                                                            exp                      ⁡                                              (                                                                              j                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                            μ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          T                              2                                                                                                      )                                                              +                                          exp                      ⁡                                              (                                                                                                            -                              j                                                        ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                            μ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          T                              2                                                                                                      )                                                                              }                                                                                        (        1        )            
Here, t, xcexc and T is a time counted from beginning of each symbol, a constant called a chirp rate, and a symbol cycle, respectively.
The radio signal arrives through transmission paths to a receiver added with a frequency shift xcex94f due to fading, for example, and therefore, the chirp signal r(t) in the received signal is expressed as follows.                                                                         r                ⁡                                  (                  t                  )                                            =                                                s                  ⁡                                      (                    t                    )                                                  ·                                  exp                  ⁡                                      (                                          j2πΔ                      ⁢                                              xe2x80x83                                            ⁢                      f                      ⁢                                              xe2x80x83                                            ⁢                      t                                        )                                                                                                                          =                                                1                                      2                                                  ⁢                                  {                                                            exp                      ⁡                                              (                                                                              j                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            πΔ                            ⁢                                                          xe2x80x83                                                        ⁢                            f                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                                                    j                              ⁢                                                              xe2x80x83                                                            ⁢                              π                              ⁢                                                              xe2x80x83                                                            ⁢                                                              t                                2                                                                                                                    μ                              ⁢                                                              xe2x80x83                                                            ⁢                                                              T                                2                                                                                                                                    )                                                              +                                          exp                      ⁡                                              (                                                                              j                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                                                          xe2x80x83                                                        ⁢                            πΔ                            ⁢                                                          xe2x80x83                                                        ⁢                            f                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    -                                                                                    j                              ⁢                                                              xe2x80x83                                                            ⁢                              π                              ⁢                                                              xe2x80x83                                                            ⁢                                                              t                                2                                                                                                                    μ                              ⁢                                                              xe2x80x83                                                            ⁢                                                              T                                2                                                                                                                                    )                                                                              }                                                                                        (        2        )            
The chirp signal generator 6 generates a reference chirp signal having the same chirp rate xcexc with the transmission signal and expressed as       exp    ⁡          (                        j          ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢                                    (                              t                +                                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                            )                        2                                    μ          ⁢                      xe2x80x83                    ⁢                      T            2                              )        ,
and its conjugate complex signal expressed as       exp    ⁡          (                                    -            j                    ⁢                      xe2x80x83                    ⁢          π          ⁢                      xe2x80x83                    ⁢                                    (                              t                +                                  Δ                  ⁢                                      xe2x80x83                                    ⁢                  t                                            )                        2                                    μ          ⁢                      xe2x80x83                    ⁢                      T            2                              )        ,
xcex94t being a difference of symbol timings. The reference chirp signal and the conjugate complex signal are multiplied onto the received signal by the demodulator 7 for obtaining following two complex signals P(t) and Q(t) (hereinafter called the in-phase complex signal and the quadrature-phase complex signal, respectively) to analyzed by the detector unit 9;                                           P            ⁡                          (              t              )                                =                                    r              ⁡                              (                t                )                                      ·                          exp              ⁡                              (                                                      j                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                                                  (                                                  t                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                                          )                                            2                                                                            μ                    ⁢                                          xe2x80x83                                        ⁢                                          T                      2                                                                      )                                                    ,                            (        3        )                                          Q          ⁡                      (            t            )                          =                              r            ⁡                          (              t              )                                ·                                    exp              ⁡                              (                                                                            -                      j                                        ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                                                  (                                                  t                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                                          )                                            2                                                                            μ                    ⁢                                          xe2x80x83                                        ⁢                                          T                      2                                                                      )                                      .                                              (        4        )            
FIG. 4 is a block diagram illustrating a configuration of the detector unit 9 of FIG. 3, comprising a complex FFT circuit 10, a power detector 11 and a comparator 12.
Each of the in-phase and the quadrature-phase complex signal P(t) and Q(t) is transformed into a frequency domain signal through the complex FFT circuit 10, whereof a power value of each frequency component is calculated by the power detector 11 and a frequency component giving a maximum power spectrum is detected by the comparator 12.
As to in-phase complex signal P(t) of equation (3), it is expressed as P(t)=A+B, where;
                              A          =                                    {                              first                ⁢                                  xe2x80x83                                ⁢                term                ⁢                                  xe2x80x83                                ⁢                of                ⁢                                  xe2x80x83                                ⁢                equation                ⁢                                  xe2x80x83                                ⁢                                  (                  2                  )                                            }                        ·                          exp              ⁡                              (                                                      j                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                                                  (                                                  t                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                                          )                                            2                                                                            μ                    ⁢                                          xe2x80x83                                        ⁢                                          T                      2                                                                      )                                                    ,                            (        5        )            
and
                              B          =                                    {                              second                ⁢                                  xe2x80x83                                ⁢                term                ⁢                                  xe2x80x83                                ⁢                of                ⁢                                  xe2x80x83                                ⁢                equation                ⁢                                  xe2x80x83                                ⁢                                  (                  2                  )                                            }                        ·                          exp              ⁡                              (                                                      j                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                                                  (                                                  t                          +                                                      Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                                          )                                            2                                                                            μ                    ⁢                                          xe2x80x83                                        ⁢                                          T                      2                                                                      )                                                    ,                            (        6        )            
The term A of equation (5) is calculated as;                                                         A              =                                                1                                      2                                                  ⁢                                  xe2x80x83                                ⁢                                                      exp                    ⁡                                          (                                                                        j                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                          πΔ                          ⁢                                                      xe2x80x83                                                    ⁢                          f                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                +                                                                              j                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                            μ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          T                              2                                                                                                                          )                                                        ·                  exp                                ⁢                                  (                                                            j                      ⁢                                              xe2x80x83                                            ⁢                      π                      ⁢                                              xe2x80x83                                            ⁢                                                                        (                                                      t                            +                                                          Δ                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                                                )                                                2                                                                                    μ                      ⁢                                              xe2x80x83                                            ⁢                                              T                        2                                                                              )                                                                                                        =                                                1                                      2                                                  ⁢                                  xe2x80x83                                ⁢                                  exp                  ⁡                                      (                                                                                                                        j                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                +                                                      j                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            t                            ⁢                                                          xe2x80x83                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                      j                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                                                μ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            2                                                                                              +                                              j                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                              )                                                                                                          (        7        )            
which is a product of exp(2jxcfx80t2) whereof frequency varies according to time passage, and therefore, the term A makes no contribution to the maximum power spectrum after FFT.
The term B of equation (5) is calculated as;                                                         B              =                                                1                                      2                                                  ⁢                                  xe2x80x83                                ⁢                                                      exp                    ⁡                                          (                                                                        j                          ⁢                                                      xe2x80x83                                                    ⁢                          2                          ⁢                          πΔ                          ⁢                                                      xe2x80x83                                                    ⁢                          f                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                -                                                                              j                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                            μ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          T                              2                                                                                                                          )                                                        ·                                      exp                    ⁡                                          (                                                                        j                          ⁢                                                      xe2x80x83                                                    ⁢                          π                          ⁢                                                      xe2x80x83                                                    ⁢                                                                                    (                                                              t                                +                                                                  Δ                                  ⁢                                                                      xe2x80x83                                                                    ⁢                                  t                                                                                            )                                                        2                                                                                                    μ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            2                                                                                              )                                                                                                                                              =                                                1                                      2                                                  ⁢                                  xe2x80x83                                ⁢                                  exp                  ⁡                                      (                                                                                                                        j                            ⁢                                                          xe2x80x83                                                        ⁢                            2                            ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            t                            ⁢                                                          xe2x80x83                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                            t                                                    +                                                      j                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            Δ                            ⁢                                                          xe2x80x83                                                        ⁢                                                          t                              2                                                                                                                                μ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            2                                                                                              +                                              j                        ⁢                                                  xe2x80x83                                                ⁢                        2                        ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                        Δ                        ⁢                                                  xe2x80x83                                                ⁢                        f                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                              )                                                                                                          (        8        )            
whereof   exp  ⁡      (                  j        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢                  t          2                            μ        ⁢                  xe2x80x83                ⁢                  T          2                      )  
is a constant term to be cancelled in the power spectrum after FFT.
Therefore, a frequency dependent component P, which defines the maximum power spectrum after FFT, of the in-phase complex signal P(t) can be expressed as follows;                     P        =                              1                          2                                ⁢                      exp            ⁡                          (                                                j2π                  ⁡                                      (                                                                  Δ                        ⁢                                                  xe2x80x83                                                ⁢                        f                                            +                                                                        Δ                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                          μ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            2                                                                                                                )                                                  ⁢                t                            )                                                          (        9        )            
In the same way, a frequency dependent component Q, which defines the maximum power spectrum after FFT, of the quadrature-phase complex signal Q(t) can be expressed as follows;                     Q        =                              1                          2                                ⁢                      exp            ⁡                          (                              j                ⁢                                  xe2x80x83                                ⁢                2                ⁢                                  xe2x80x83                                ⁢                                  π                  ⁡                                      (                                                                  Δ                        ⁢                                                  xe2x80x83                                                ⁢                        f                                            -                                                                        Δ                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                                          μ                          ⁢                                                      xe2x80x83                                                    ⁢                                                      T                            2                                                                                                                )                                                  ⁢                t                            )                                                          (        10        )            
Therefore, the frequency domain signal of the in-phase complex signal P(t) after processed by the complex FFT circuit 10 has a power spectrum peak at a frequency Fp=xcex94f   Fp  =            Δ      ⁢              xe2x80x83            ⁢      f        +                  Δ        ⁢                  xe2x80x83                ⁢        t                    μ        ⁢                  xe2x80x83                ⁢                  T          2                    
as shown in FIG. 5A, while that of the complex signal Q(t) has a power spectrum peak at a frequency Fq=xcex94f   Fp  =            Δ      ⁢              xe2x80x83            ⁢      f        -                  Δ        ⁢                  xe2x80x83                ⁢        t                    μ        ⁢                  xe2x80x83                ⁢                  T          2                    
as shown in FIG. 5B, which are detected by the comparator 12.
From these frequencies Fp and Fq, the frequency shift xcex94f and the difference of symbol timing At are calculated as follows;
xcex94f=(Fp+Fq)/2,xe2x80x83xe2x80x83(11)
xcex94t=(Fpxe2x88x92Fq)xc2x7xcexcT2/2,xe2x80x83xe2x80x83(12)
According to the frequency shift xcex94f and the difference xcex94t of the symbol timings thus obtained, the frequency and timing synchronization is performed in the conventional frequency and timing synchronization circuit 104 of FIG. 3 making use of the chirp signal.
However, there is a problem of frequency resolution of the complex FFT circuit 10 in the conventional frequency and timing synchronization circuit 104 of FIG. 3, when the C/N ratio of the received signal is low.
FIG. 6 is a spectrum chart for illustrating the above problem, whereof Y-axis represents frequency offset to a reference frequency and X-axis represents a power value of a signal according to the frequency offset. The resolution of the FFT processing is determined by the sampling frequency fs and the number m of samples, and a vector value is calculated for each frequency component ranged with a frequency difference fs/m, as represented by black dots in FIG. 6.
Therefore, when a signal has a peak value p at the same frequency with the reference frequency or at a frequency just shifted by n (n being an integer) times of fs/m from the reference frequency as illustrated in FIG. 6 with a dashed line denoted as Best Case, the peak value p is output as it is, at the frequency component. However, when the signal has the peak value p at a frequency in a middle of two consecutive resolution steps of the FFT as illustrated with a solid line denoted as Worst Case, the peak value p is to be represented by two off-peak values a of two frequency components nearest to the frequency offset fp giving the peak value p, that is, frequency components having frequency offsets 0 and +fs/m, in the example of FIG. 6.
Therefore, when the signal has a sufficient C/N ratio, the actual offset fp of the peak frequency can be estimated to be fp=+fs/2m, in the example, from frequency offsets 0 and +fs/m of the two off-peak values xcex1. However, when the C/N ratio is low, the off-peak values xcex1 may become equivalent to the noise level and become impossible to be detected by the comparator 12.
This is the problem.
Therefore, a primary object of the present invention is to deal with the above problem and provide a frequency and timing synchronization circuit which can surely detect the frequency shift and the timing difference of a received signal making use of the chirp signal, even when the C/N ratio of the received signal is low.
In order to achieve the object, a frequency and timing synchronization circuit making use of a chirp signal according to the invention, for detecting a frequency shift and a synchronization timing of a received signal modulated with a transmission chirp signal, comprises:
a chirp signal generator for generating a reference chirp signal having the same chirp rate with the transmission chirp signal and a conjugate complex signal of the reference chirp signal;
a first demodulator for obtaining a first in-phase complex signal and a first quadrature-phase complex signal by demodulating the received signal with the reference chirp signal and the conjugate complex signal, respectively;
a frequency offset circuit for obtaining an offset signal by shifting a frequency of the received signal by an offset frequency;
a second demodulator for obtaining a second in-phase complex signal and a second quadrature-phase complex signal by demodulating the offset signal with the reference chirp signal and the conjugate complex signal, respectively; and
a detector unit for detecting the frequency shift and the synchronization timing according to a first and a second peak frequency, the first peak frequency giving a maximum power spectrum among frequency components of the first and the second in-phase complex signal, and the second peak frequency giving a maximum power spectrum among frequency components of the first and the second quadrature-phase complex signal.
a detector unit for detecting the frequency shift and a difference of the synchronization timing according to a first peak frequency giving a maximum power spectrum among frequency components of the first and the second in-phase complex signal after processed through FFT, and a second peak frequency giving a maximum power spectrum among frequency components of the first and the second quadrature-phase complex signal after processed through FFT.
The offset frequency is determined in consideration of resolution of the complex FFT circuit defined by a sampling frequency and a number of samples applied in the complex FFT circuit.
Therefore, the effective resolution step of the FFT can be made fine, and the frequency shift and the timing difference of a received signal can be detected surely and exactly making use of the chirp signal, even when the C/N ratio of the received signal is low.
In place of the frequency offset circuit and the second demodulator, there may be comprised:
a plurality of frequency offset circuits each obtaining respective one of offset signals by shifting a frequency of the received signal by a distinct offset frequency; and
second demodulators each obtaining respective one of offset in-phase complex signals and respective one of offset quadrature-phase complex signals by demodulating respective one of the offset signals with the reference chirp signal and the conjugate complex signal, respectively.
In this case, the first peak frequency is detected from a frequency component giving a maximum power spectrum among frequency components of the first in-phase complex signal and the offset in-phase complex signals after processed through FFT, and a second peak frequency is detected from a frequency component giving a maximum power spectrum among frequency components of the first quadrature-phase complex signal and the offset quadrature-phase complex signals after processed through FFT.